In radar and active sonar processing the Doppler compressed versions of the transmitted waveform are used as candidate replicas for replica correlation at the receiver. The received signal is convolved with various replicas. The replicas are time compressed (or time dilated) to account for possible Doppler compressions (or dilations) in the signal. A target's relative Doppler is estimated by the Doppler and range-lag of the replica which correlates best with the target's echo. This Doppler compressed replica-correlation process is known as matched-filtering. It is well known that this process produces peak outputs having a maximum signal-to-noise ratio (SNR) in the case of white additive noise. It is also known that in the case of colored noise the process with maximum SNR is that which first whitens the noise then match filters to the whitened version of the waveform. In the general radar and sonar situations, the spectrum of the noise is not known, and is in fact, highly variable. Conventional radar and sonar coherent processors' matched-filters are designed under the white noise assumption.
The detection of low-Doppler targets in the neighborhood of clutter is generally performed using MTI filters which attempt to filter the zero-Doppler clutter. A problem is knowing exactly where zero-Doppler is. Also, fixed MTI filters cannot respond to changing environments, and adaptive MTI filters are generally of a fixed structure applicable to zero-Doppler clutter response only, and not applicable to the general range-Doppler situation (i.e., to any range-Doppler cell in the range-Doppler plane).